(CNSNews.com) - Sen. Chuck Schumer (D-N.Y.) said he won't let the terror attack in Boston -- and concerns about the immigrants behind it -- derail the immigration bill introduced last week by Sens. Chuck Schumer (D-N.Y.), Lindsey Graham (R-S.C.) and six other senators.

"There are some -- some on the hard right...who opposed our immigration bill from the get-go, and they're using this as an excuse. We are not going to let them do that," Schumer told CNN's "State of the Union" on Sunday.

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"If they have a reason, a suggestion as to how to change it based on what happened in Boston, we'll certainly be open to it. But we're not going to let them use what happened in Boston as an excuse, because our law toughens things up."

Graham said "now is the time" to find out about the 11 million people who are in the country illegally: "Most of them are here to work, but we may find some terrorists in our midst who have been hiding in the shadows.

"When it comes to the entry/exit visa system, the 19 hijackers were all students who overstayed their visas, and the system didn't capture that. We're going to fix that," Graham said. "In our bill, when you come into the country, it goes into the system, and when your time to leave the country expires and you haven't left, law enforcement is notified."

Graham said what happened in Boston "should urge us to act quicker, not slower when it comes to getting the 11 million identified."

Sen. Schumer agreed: "Certainly keeping the status quo is not a very good argument, given what happened. And let me say a couple of things. Our law toughens things up, as Lindsey mentioned, making the 11 million register, having a system when you come in on a visa they know when you're supposed to leave and track you down if you don't, and in fact asylum which the Tsarnaev family came here on, was greatly toughened up a few years after. They might not have gotten asylum under the present law."

Graham said that what happened in Boston is "no excuse to stop immigration reform, to secure our borders, control who comes and gets a job and to create order out of chaos. We need to move on," he said.

Schumer said there will be "ample opportunity" to amend the bill produced by the so-called gang of either. "First, it's online now, it's going to be online for three weeks before we even get to the Judiciary Committee markup. There anyone, including two of the leading opponents of immigration reform, Senator Sessions and Grassley, both of whom have said this is a reason to slow it down, can make any amendments they want. And then we go to the floor. Any one of the 100 senators could propose amendments.

"To not do it or to say do it six months from now is an excuse. There's ample opportunity to amend the bill if people see anything that they'd want to toughen up even further than what we have done."

On "Fox News Sunday," Rep. Pete King (R-N.Y.) agreed that what happened in the Boston area last week shouldn't derail immigration reform:

"Well, first of all, I don't think it should have a severe impact on the immigration debate. I do think it should focus on whether or not it should be refined, and that if people are coming from a country which has terrorist background, if there's a strong terrorist element in that country, that there should be extra vetting for people from that country.

"But, listen, I'm a grandson of immigrants," Rep. King said. "While I have some concerns with the security aspects of immigration reform, I don't think we should use that as an excuse to stop the debate. But I do believe that, again, if someone's coming from a country which has strong al-Qaida or any other type of terrorist element in it, that we should not be afraid to ask the extra questions or the extra research, do the extra vetting to make sure that people coming in here have no affiliation at all to those terrorist groups."